Elasto-Viscoplastic Properties of Aa2017

TASK QUARTERLY 15 No 1, 5–20 ELASTO-VISCOPLASTIC PROPERTIES OF AA2017 ALUMINIUM ALLOY ANDRZEJ AMBROZIAK, PAWEŁ KŁOSOWSKI AND ŁUKASZ PYRZOWSKI Department of Structural Mechanics and Bridge Structures, Faculty of Civil and Environmental Engineering, Gdansk University of Technology, Narutowicza 11/12, 80-233 Gdansk, Poland ambrozan, klosow, lpyrzow @pg.gda.pl { } (Received 18 November 2010; revised manuscript received 21 February 2011) Abstract: This paper describes a procedure for the identification of material parameters for the elasto-viscoplastic Bodner-Partom model. A set of viscoplastic parameters is identified for AA2017 aluminium alloy. The evaluation of material parameters for the Bodner-Partom constitutive equations is carried out using tensile tests. Numerical simulations of material behaviour during constant strain-rate tests are compared with direct uniaxial tensile experiments. A review of the models applied to concisely describe aluminium alloy is also given. Keywords: AA2017, viscoplasticity, Bodner-Partom, tensile tests 1. Introduction Aluminium alloy is commonly used in the aircraft industry, building and construction industry, electricity, packaging, transportation, etc. It is an alloy of intermediate strength and good ductility. The main alloying elements are copper, magnesium, zinc, silicon, manganese and lithium. In the case of AA2017 aluminium alloy, the main alloying element is copper, see e.g. [1]. The selection of constitutive models is one of the most important prob- lems, which is considered before other aspects of structural analysis. Different approaches to constitutive modelling of the behaviour of aluminium alloys (such as nonlinear elastic, viscoplastic, viscoelastic) can be considered. Very often, the undertaken approach depends not only on the material properties, but also on the type of loading under consideration. In 1943, Ramberg and Osgood [2] proposed an elasto-plastic model for the description of the behaviour of aluminium alloy, stainless steel and carbon steel. This model is used in many practical engineering applications. Kuruppu et al. [3] tq115a-e/5 8 V 2012 BOP s.c., http://www.bop.com.pl 6 A. Ambroziak et al. presented an extension of the Ramaswamy, Stouffer, and Laflen unified elastic- viscoplastic theory to the description of the strain-rate insensitive 7050-T7451 aluminium alloy. Kowalewski et al. [4] described the creep behaviour of aluminium alloy at 150◦C by constitutive equations using a hyperbolic sine function of stress. Two mechanisms were identified by Kowalewski et al. [4]: creep-constrained cavitation and the ageing of particulate microstructure. Gelin and Ghouati [5] applied the inverse identification method to identify the viscoplastic parameters of aluminium alloy. Santhanam [6] used an elastic-viscoplastic constitutive model with an isotropic internal variable to describe the behaviour of aluminium alloy during hot-forming. Zhao and Lee [7] described simulation springback. Material parameters of 6022-T4 aluminium sheets were identified by an inverse method. Lauro et al. [8] presented an identification procedure for the damage parameters for aluminium. An inverse method consists in correlating the experimental and numerical measurements with a tensile test on a notched specimen. Omersphanic et al. [9] identified material parameters for high-strength steel alloys ZSte340 and DP600 and for AA5182 aluminium alloy. Mart´ınez et al. [10] described the constitutive model for low temperatures and the plastic strain rates for the cold forming of 2117-T4 alloy. The parameters of the Hansel-Spittel and hyperboloid-type models were also identified. Diot et al. [11] described the 1 rheological characterisation of Al-Mg alloy at strain rates from 0.01 to 10 s− , at temperatures from 423 to 673 K. Omerspahic [12] determines damage propagation in ZSte340 high-strength steel alloy and in AA5182 aluminium alloy sheets. The approach for the identification of the isotropic material damage parameters is based on continuous uniaxial tensile loading and unloading of metal sheets. A global optimization technique was used by Majak et al. [13] to determine the material parameters of AA6181-T4 aluminium alloy sheets. Chaparro et al. [14] employed a genetic algorithm and a gradient-based algorithm to determine the material parameters of EN AW-5754 aluminium alloy. Bauffioux et al. [15] developed an inverse method for adjusting the material parameters in single point incremental forming. In [15], AA3103-O aluminium alloy is examined. Zhang et al. [16] described the material behaviour of 5083 aluminium alloy at high temperatures (150, 240 and 300◦C). Swift hardening law was used to describe the visco-plastic behaviour of the alloy. It should be noted that the particularities of the process for the determination of the material parameters can vary in each case. This process is sensitive to the initial values of the parameters. Thus, it is possible to obtain different values of the parameters for the same material. These different set of parameters can exactly describe behaviour of aluminium alloy. 2. Laboratory tests We carried out experiments with AA2017 aluminium alloy at room tem- 4 1 perature, using five different values for the constant strain rates:ε ˙ =1 10− s− , 4 1 3 1 3 1 2 1 · ε˙ =5 10− s− ,ε ˙ =1 10− s− ,ε ˙ =1 5− s− ,ε ˙ =1 10− s− . Two types of spec- · · · · tq115a-e/6 8 V 2012 BOP s.c., http://www.bop.com.pl Elasto-Viscoplastic Properties of AA2017 Aluminium Alloy 7 imens were examined – one cut along and one across the rolling direction of the sheet. The specimens were 15cm long, 1.2cm wide, and 0.1cm thick. All uniaxial experiments were performed using a Zwick/Roell Z020 Universal Testing Machine equipped with an extensometer. The clamp spacing was set to 7.5cm, whereas the gauge length was 4.0cm (see Figure 1). Figure 1. Experimental stand 3. Determination of elastic material parameters First, we transformed the displacement-force data obtained from the measurements to obtain the strain-stress relationship. The engineering strain and stress were used. Initially, the elastic tensile modulus E was determined for the specimens of AA2017, using linear approximation (column 2 of Table 1 and Table 2). The elastic tensile modulus in the strain range of ε 0, 0.003 was specified. ∈ Subsequently, the inelastic strain εI was calculated as: σ εI = ε (1) − E where ε is the total strain and σ is the stress. It was assumed that when the inelastic strain exceeds zero, the yield limit value is reached (see Table 1 and Table 2). The obtained results indicate that the magnitude of viscous effects is small, nevertheless, an elasto-viscoplastic constitutive model can be applied, particularly tq115a-e/7 8 V 2012 BOP s.c., http://www.bop.com.pl 8 A. Ambroziak et al. Table 1. Values of the elasticity modulus and the yield limit for the specimen cut across the rolling direction of the sheet ε˙ E σγ E [MPa] σγ [MPa] 1 [s− ] [MPa] [MPa] mean values mean values 0.0001 67 525 228.0 67 525 0 228.0 0 ± ± 68 546 227.4 0.0005 68 277 380 229.3 2.7 68 007 231.2 ± ± 68 590 230.6 0.001 69 737 1621 232.2 2.3 70 883 233.9 ± ± 69 045 238.2 0.005 69 105 84 238.3 0.2 69 164 238.4 ± ± 69 837 235.5 0.01 69 226 864 233.0 3.5 68 615 230.5 ± ± Table 2. Values of the elasticity modulus and the yield limit for the specimen cut along the rolling direction of the sheet ε˙ E σγ E [MPa] σγ [MPa] 1 [s− ] [MPa] [MPa] mean values mean values 0.0001 69 812 251.66 69 812 0 251.7 0 ± ± 70 666 249.18 0.0005 70 704 54 251.8 3.7 70 743 254.38 ± ± 71 000 254.5 0.001 71 258 364 255.4 1.3 71 516 256.4 ± ± 71 903 254.8 0.005 70 995 1284 253.7 1.5 70 087 252.7 ± ± 71 229 257.9 0.01 70 754 671 256.9 1.3 70 279 256.0 ± ± so in the case of either long-lasting or very rapid loads. On the other hand, certain authors deemed viscous effects negligible and, therefore, applied elasto-plastic constitutive models to describe aluminium alloys. Although the rolling direction was observed to have a small influence on the yield limit, the authors of the present paper have decided to apply isotropic modelling. On the basis of the mean values of the yield limit σγ , the elastic tensile modulus E was determined (see Table 3). A graphical visualization of the distribution of the mean yield limit is shown in Figure 2. 4. Description of the constitutive model From a wide range of available viscoplastic constitutive models, the Bodner- Partom model [17] was chosen. This model belongs to a group of isotropic constitutive models, which are used to describe the elasto-viscoplastic behaviour tq115a-e/8 8 V 2012 BOP s.c., http://www.bop.com.pl Elasto-Viscoplastic Properties of AA2017 Aluminium Alloy 9 Table 3. Mean values of the elasticity modulus and the yield limit ε˙ σγ E 1 [s− ] [MPa] [MPa] 0.0001 239.8 0.0005 240.5 0.001 243.8 69 700 0.005 246.0 0.01 245.0 Figure 2. Conventional yield limit – on a linear scale of materials for small inelastic deformations and small strain rates (since the model is additive), see e.g. [18]. First, an additive decomposition of the total strain rate ε˙ (for small strain 1 ratesε ˙ < 0.1s− ) was assumed: ε˙ = ε˙E +ε˙I (2) where ε˙E and ε˙I are the elastic and inelastic strain rate, respectively. The relation between the stress rate σ˙ and the strain rate ε˙E, for the assumed isotropic material, was defined as: σ˙ = D ε˙E = D (ε˙ ε˙I ) (3) · · − where D is the standard elasticity tensor.

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